What is the extreme f(x)=3xln(x)-8x,x>0 ?

The extreme f(x)=3xln(x)-8x,x>0 is Minimum(e^{5/3},-3e^{5/3})

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extreme f(x)=3xln(x)-8x,x>0

extreme

Minimum (e^{\frac{5}{3}}, - 3 e^{\frac{5}{3}})

Solution steps

Find the critical points:

x = e^{\frac{5}{3}}

Domain of

3 x ln (x) - 8 x, x > 0 : x > 0

Find intervals:

Decreasing

: 0 < x < e^{\frac{5}{3}},

Increasing

: e^{\frac{5}{3}} < x < \infty

Plug the extreme point

x = e^{\frac{5}{3}}

into

3 x ln (x) - 8 x \Rightarrow y = - 3 e^{\frac{5}{3}}

Minimum (e^{\frac{5}{3}}, - 3 e^{\frac{5}{3}})

What is the extreme f(x)=3xln(x)-8x,x>0 ?
The extreme f(x)=3xln(x)-8x,x>0 is Minimum(e^{5/3},-3e^{5/3})